TSTP Solution File: ANA009-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : ANA009-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 10:08:45 EDT 2023
% Result : Unsatisfiable 8.63s 2.91s
% Output : Refutation 8.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 352
% Syntax : Number of formulae : 652 ( 139 unt; 53 typ; 0 def)
% Number of atoms : 1199 ( 214 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 4336 ( 596 ~; 600 |; 0 &;3140 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 53 usr; 8 con; 0-3 aty)
% Number of variables : 922 ( 0 ^; 922 !; 0 ?; 922 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_lb_type,type,
v_lb: $i > $i ).
thf(v_f_type,type,
v_f: $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(c_plus_type,type,
c_plus: $i > $i > $i > $i ).
thf(v_g_type,type,
v_g: $i > $i ).
thf(c_0_type,type,
c_0: $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_uminus_type,type,
c_uminus: $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_less_type,type,
c_less: $i > $i > $i > $o ).
thf(tc_IntDef_Oint_type,type,
tc_IntDef_Oint: $i ).
thf(c_IntDef_Oof__int_type,type,
c_IntDef_Oof__int: $i > $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_Numeral_Onumber__of_type,type,
c_Numeral_Onumber__of: $i > $i > $i ).
thf(c_Nat_Opower_type,type,
c_Nat_Opower: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le_type,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__abs_type,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(c_HOL_Oabs_type,type,
c_HOL_Oabs: $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_times_type,type,
c_times: $i > $i > $i > $i ).
thf(tc_set_type,type,
tc_set: $i > $i ).
thf(c_IntDef_Oneg_type,type,
c_IntDef_Oneg: $i > $i > $o ).
thf(c_emptyset_type,type,
c_emptyset: $i ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__mult_type,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
thf(class_OrderedGroup_Oab__semigroup__mult_type,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group_type,type,
class_OrderedGroup_Olordered__ab__group: $i > $o ).
thf(c_LOrder_Omeet_type,type,
c_LOrder_Omeet: $i > $i > $i > $i ).
thf(c_LOrder_Ojoin_type,type,
c_LOrder_Ojoin: $i > $i > $i > $i ).
thf(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__join_type,type,
class_OrderedGroup_Olordered__ab__group__join: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(class_OrderedGroup_Olordered__ab__group__meet_type,type,
class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).
thf(class_LOrder_Ojoin__semilorder_type,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
thf(class_LOrder_Omeet__semilorder_type,type,
class_LOrder_Omeet__semilorder: $i > $o ).
thf(class_OrderedGroup_Ocomm__monoid__add_type,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(class_Ring__and__Field_Opordered__comm__semiring_type,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
thf(class_OrderedGroup_Oordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
thf(class_LOrder_Olorder_type,type,
class_LOrder_Olorder: $i > $o ).
thf(c_List_Odrop_type,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oaxclass__abs__if_type,type,
class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).
thf(class_Ring__and__Field_Opordered__semiring_type,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
thf(class_OrderedGroup_Opordered__cancel__ab__semigroup__add_type,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(c_List_Ochar_OChar_type,type,
c_List_Ochar_OChar: $i > $i > $i ).
thf(c_OrderedGroup_Onprt_type,type,
c_OrderedGroup_Onprt: $i > $i > $i ).
thf(class_Ring__and__Field_Oaxclass__no__zero__divisors_type,type,
class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).
thf(c_OrderedGroup_Opprt_type,type,
c_OrderedGroup_Opprt: $i > $i > $i ).
thf(c_List_Oupt_type,type,
c_List_Oupt: $i > $i > $i ).
thf(class_Ring__and__Field_Oaxclass__0__neq__1_type,type,
class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).
thf(c_Nat_Osize_type,type,
c_Nat_Osize: $i > $i > $i ).
thf(tc_List_Ochar_type,type,
tc_List_Ochar: $i ).
thf(c_List_Olexn_type,type,
c_List_Olexn: $i > $i > $i > $i ).
thf(171,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_HOL_Oabs @ B @ A ) @ A )
= ( c_HOL_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
thf(645,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_HOL_Oabs @ B @ A ) @ A )
= ( c_HOL_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(252,axiom,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
thf(809,plain,
! [A: $i] : ( c_lessequals @ c_0 @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
thf(365,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
thf(628,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_plus @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(288,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_IntDef_Oof__int @ c_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
thf(893,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_IntDef_Oof__int @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
thf(468,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(182,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
thf(666,plain,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ochar_OChar @ A @ B )
!= ( c_List_Ochar_OChar @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
thf(481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ochar_OChar @ A @ B )
!= ( c_List_Ochar_OChar @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
thf(352,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_less @ A @ B @ ( tc_set @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
thf(408,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_less @ A @ B @ ( tc_set @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(222,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
thf(741,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
thf(379,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(175,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
thf(655,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ tc_IntDef_Oint )
| ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
thf(597,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ B @ tc_IntDef_Oint )
| ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(274,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
thf(861,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ c_0 @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
thf(582,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ c_0 @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_plus @ D @ B @ A ) @ ( c_plus @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
thf(762,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_plus @ D @ B @ A ) @ ( c_plus @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(156,axiom,
! [B: $i,A: $i] : ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
thf(614,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( ( c_LOrder_Omeet @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
thf(677,plain,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Omeet__semilorder @ A )
| ( ( c_LOrder_Omeet @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
thf(385,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
thf(472,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
| ( c_lessequals @ B @ C @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ c_0 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
thf(814,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ c_0 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(198,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
thf(698,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(225,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_lessequals @ ( c_plus @ B @ C @ A ) @ ( c_plus @ D @ C @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
thf(747,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_lessequals @ ( c_plus @ B @ C @ A ) @ ( c_plus @ D @ C @ A ) @ A )
| ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(20,axiom,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
thf(340,plain,
! [A: $i] :
~ ( c_less @ A @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(184,axiom,
class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
thf(670,plain,
class_Ring__and__Field_Opordered__comm__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).
thf(898,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(240,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_OrderedGroup_Opprt @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
thf(782,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_OrderedGroup_Opprt @ B @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(204,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
thf(709,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(57,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_15) ).
thf(417,plain,
! [A: $i] :
( ( class_OrderedGroup_Ocomm__monoid__mult @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(2,negated_conjecture,
! [A: $i] : ( c_lessequals @ ( v_f @ A ) @ ( c_plus @ ( v_lb @ A ) @ ( v_g @ A ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(301,plain,
! [A: $i] : ( c_lessequals @ ( v_f @ A ) @ ( c_plus @ ( v_lb @ A ) @ ( v_g @ A ) @ t_b ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(130,axiom,
class_LOrder_Omeet__semilorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
thf(565,plain,
class_LOrder_Omeet__semilorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ ( c_plus @ B @ B @ A ) @ A )
| ( c_lessequals @ c_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
thf(785,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ ( c_plus @ B @ B @ A ) @ A )
| ( c_lessequals @ c_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_less @ ( c_uminus @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).
thf(344,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_less @ ( c_uminus @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(119,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
thf(542,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(142,axiom,
class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
thf(587,plain,
class_OrderedGroup_Olordered__ab__group__abs @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_times @ C @ B @ tc_nat ) )
| ( A = C )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
thf(619,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_times @ C @ B @ tc_nat ) )
| ( A = C )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(298,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).
thf(917,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
thf(751,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(127,axiom,
! [A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
thf(559,plain,
! [A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(638,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_uminus @ ( c_LOrder_Omeet @ B @ C @ A ) @ A )
= ( c_LOrder_Ojoin @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
thf(421,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_uminus @ ( c_LOrder_Omeet @ B @ C @ A ) @ A )
= ( c_LOrder_Ojoin @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ A @ C @ tc_nat ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
thf(606,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ A @ C @ tc_nat ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A )
| ( c_less @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(71,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
thf(448,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(256,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
thf(817,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(292,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Ojoin @ B @ ( c_uminus @ B @ A ) @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
thf(902,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Ojoin @ B @ ( c_uminus @ B @ A ) @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(94,axiom,
class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
thf(492,plain,
class_OrderedGroup_Ocomm__monoid__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( c_lessequals @ ( c_uminus @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
thf(789,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( c_lessequals @ ( c_uminus @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_plus @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) @ A )
= ( c_plus @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
thf(443,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_plus @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) @ A )
= ( c_plus @ ( c_HOL_Oabs @ B @ A ) @ ( c_HOL_Oabs @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
thf(321,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Numeral_Onumber__of @ A @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
thf(376,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ B @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Numeral_Onumber__of @ A @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(91,axiom,
class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
thf(485,plain,
class_OrderedGroup_Omonoid__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_less @ ( c_plus @ B @ C @ A ) @ ( c_plus @ B @ D @ A ) @ A )
| ( c_less @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_0) ).
thf(348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_less @ ( c_plus @ B @ C @ A ) @ ( c_plus @ B @ D @ A ) @ A )
| ( c_less @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(258,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_1) ).
thf(821,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_plus @ B @ c_0 @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).
thf(905,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_plus @ B @ c_0 @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(89,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
thf(480,plain,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(151,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
thf(602,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(46,axiom,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
thf(397,plain,
! [B: $i,A: $i] :
~ ( c_less @ A @ c_emptyset @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(237,axiom,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_2) ).
thf(774,plain,
( ( c_plus @ c_0 @ c_0 @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(178,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
thf(660,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
| ( c_less @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
thf(411,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
| ( c_less @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(102,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
thf(507,plain,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(281,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ c_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
thf(877,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ ( c_uminus @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ c_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(196,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Opprt @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
thf(692,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Opprt @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(112,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
thf(527,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_less @ ( c_plus @ D @ B @ A ) @ ( c_plus @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_1) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_less @ ( c_plus @ D @ B @ A ) @ ( c_plus @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_1) ).
thf(307,plain,
~ ( c_less @ c_0 @ c_0 @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(73,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
thf(452,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(299,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( c_lessequals @ ( c_plus @ B @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
thf(920,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( c_lessequals @ ( c_plus @ B @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(67,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
= ( c_HOL_Oabs @ c_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_1) ).
thf(439,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
= ( c_HOL_Oabs @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(113,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).
thf(529,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(179,axiom,
class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
thf(661,plain,
class_Ring__and__Field_Oordered__idom @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(245,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
thf(793,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ( c_List_Odrop @ c_0 @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
thf(810,plain,
! [B: $i,A: $i] :
( ( c_List_Odrop @ c_0 @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(39,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
thf(381,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(116,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
thf(534,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(247,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).
thf(798,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
thf(910,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(3,negated_conjecture,
~ ( c_lessequals @ c_0 @ ( c_plus @ ( v_f @ v_x ) @ ( c_uminus @ ( v_lb @ v_x ) @ t_b ) @ t_b ) @ t_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(302,plain,
~ ( c_lessequals @ c_0 @ ( c_plus @ ( v_f @ v_x ) @ ( c_uminus @ ( v_lb @ v_x ) @ t_b ) @ t_b ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(128,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
thf(561,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ~ ( c_less @ c_0 @ C @ tc_nat )
| ( c_less @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ~ ( c_less @ c_0 @ C @ tc_nat )
| ( c_less @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(60,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
thf(424,plain,
class_OrderedGroup_Omonoid__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( ( c_LOrder_Ojoin @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
thf(429,plain,
! [B: $i,A: $i] :
( ~ ( class_LOrder_Ojoin__semilorder @ A )
| ( ( c_LOrder_Ojoin @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(216,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
thf(729,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(82,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
thf(467,plain,
class_Ring__and__Field_Opordered__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ B @ c_0 @ A )
| ( c_less @ c_0 @ ( c_uminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
thf(361,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ B @ c_0 @ A )
| ( c_less @ c_0 @ ( c_uminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(282,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_HOL_Oabs @ B @ A )
= ( c_uminus @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
thf(879,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_HOL_Oabs @ B @ A )
= ( c_uminus @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( c_less @ c_0 @ ( c_Nat_Opower @ A @ B @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(78,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
thf(461,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(95,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
thf(493,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(190,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
thf(682,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(205,axiom,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
thf(710,plain,
class_Ring__and__Field_Opordered__semiring @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(268,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_OrderedGroup_Onprt @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
thf(847,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( ( c_OrderedGroup_Onprt @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(131,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
thf(566,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(270,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
thf(852,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(65,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
thf(435,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(109,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
thf(522,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(262,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ B @ c_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
thf(830,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
= ( c_times @ B @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(75,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).
thf(456,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_lessequals @ ( c_plus @ B @ C @ A ) @ ( c_plus @ B @ D @ A ) @ A )
| ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
thf(842,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_lessequals @ ( c_plus @ B @ C @ A ) @ ( c_plus @ B @ D @ A ) @ A )
| ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_plus @ B @ ( c_uminus @ B @ A ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
thf(874,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_plus @ B @ ( c_uminus @ B @ A ) @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(10,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ c_0 @ ( c_HOL_Oabs @ c_0 @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
thf(317,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ c_0 @ ( c_HOL_Oabs @ c_0 @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(173,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
thf(650,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(157,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
thf(615,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(213,axiom,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_17) ).
thf(725,plain,
class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
thf(403,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ A @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
thf(388,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ c_0 @ B @ A )
| ( c_less @ ( c_uminus @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
thf(356,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ c_0 @ B @ A )
| ( c_less @ ( c_uminus @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(278,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Omeet @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
thf(869,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Omeet @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(98,axiom,
! [A: $i] :
( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_13) ).
thf(499,plain,
! [A: $i] :
( ( class_OrderedGroup_Oab__semigroup__mult @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
thf(519,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ ( c_plus @ B @ C @ A ) @ A )
= ( c_plus @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
thf(742,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ ( c_plus @ B @ C @ A ) @ A )
= ( c_plus @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_plus @ B @ D @ A ) @ ( c_plus @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
thf(884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_plus @ B @ D @ A ) @ ( c_plus @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(169,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).
thf(642,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_uminus @ ( c_LOrder_Ojoin @ B @ C @ A ) @ A )
= ( c_LOrder_Omeet @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
thf(489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_uminus @ ( c_LOrder_Ojoin @ B @ C @ A ) @ A )
= ( c_LOrder_Omeet @ ( c_uminus @ B @ A ) @ ( c_uminus @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(144,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
thf(590,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(121,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
| ( c_less @ B @ c_0 @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
thf(547,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
| ( c_less @ B @ c_0 @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(202,axiom,
class_LOrder_Ojoin__semilorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
thf(706,plain,
class_LOrder_Ojoin__semilorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
thf(554,plain,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(228,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
thf(753,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(193,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
thf(686,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(87,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
thf(476,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(160,axiom,
! [A: $i] :
( ( class_OrderedGroup_Ocomm__monoid__add @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_12) ).
thf(622,plain,
! [A: $i] :
( ( class_OrderedGroup_Ocomm__monoid__add @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(200,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
thf(701,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(106,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
thf(515,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__abs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(220,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
thf(738,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(211,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
thf(721,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
| ( c_less @ c_0 @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
thf(569,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
| ( c_less @ c_0 @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
thf(779,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
thf(371,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(100,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
thf(503,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_uminus @ B @ A ) @ A )
= ( c_HOL_Oabs @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
thf(633,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ ( c_uminus @ B @ A ) @ A )
= ( c_HOL_Oabs @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(250,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
thf(805,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(103,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
thf(508,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(176,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).
thf(657,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(126,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
thf(558,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(186,axiom,
class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
thf(674,plain,
class_OrderedGroup_Olordered__ab__group__join @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(114,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
thf(530,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(180,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
thf(662,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oaxclass__abs__if @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(209,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
thf(718,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(286,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Omeet @ B @ ( c_uminus @ B @ A ) @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
thf(888,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Omeet @ B @ ( c_uminus @ B @ A ) @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(61,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
thf(425,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(105,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
thf(513,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(259,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
thf(824,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(272,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ c_0 @ ( c_uminus @ B @ A ) @ A )
| ( c_lessequals @ B @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
thf(856,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ c_0 @ ( c_uminus @ B @ A ) @ A )
| ( c_lessequals @ B @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
| ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
thf(745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( c_uminus @ C @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
| ( c_lessequals @ C @ A @ ( tc_set @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
thf(573,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ B @ tc_nat ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(689,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= ( c_plus @ C @ B @ tc_nat ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(218,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
thf(733,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( ( c_HOL_Oabs @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(140,axiom,
class_HOL_Ominus @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
thf(584,plain,
class_HOL_Ominus @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint )
| ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
thf(819,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint )
| ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ C @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
thf(579,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ B @ C @ tc_IntDef_Oint )
| ( c_lessequals @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(54,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_0 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
thf(413,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ A @ tc_IntDef_Oint ) @ c_0 @ tc_IntDef_Oint ) @ tc_IntDef_Oint ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
thf(826,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ ( c_uminus @ B @ ( tc_set @ C ) ) @ ( c_uminus @ A @ ( tc_set @ C ) ) @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(206,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs @ c_0 @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
thf(711,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ ( c_HOL_Oabs @ c_0 @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(168,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(641,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_uminus @ C @ ( tc_set @ B ) ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
thf(713,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_uminus @ A @ ( tc_set @ B ) )
!= ( c_uminus @ C @ ( tc_set @ B ) ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
thf(335,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_less @ c_0 @ B @ tc_nat )
| ( c_less @ c_0 @ ( c_times @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ~ ( c_less @ c_0 @ C @ tc_nat )
| ( c_less @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
thf(350,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ~ ( c_less @ c_0 @ C @ tc_nat )
| ( c_less @ ( c_times @ C @ A @ tc_nat ) @ ( c_times @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(118,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
thf(540,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(155,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
| ( A = c_emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
thf(611,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ c_emptyset @ ( tc_set @ B ) )
| ( A = c_emptyset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(242,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
| ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
thf(787,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_lessequals @ c_0 @ ( c_IntDef_Oof__int @ B @ A ) @ A )
| ( c_lessequals @ c_0 @ B @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(58,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
thf(419,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
thf(736,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(4,negated_conjecture,
class_Ring__and__Field_Oordered__idom @ t_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
thf(303,plain,
class_Ring__and__Field_Oordered__idom @ t_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(149,axiom,
class_LOrder_Olorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
thf(599,plain,
class_LOrder_Olorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(275,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
thf(863,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__join @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(233,axiom,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
!= ( c_IntDef_Oof__int @ B @ A ) )
| ( c_0 = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
thf(764,plain,
! [B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_0
!= ( c_IntDef_Oof__int @ B @ A ) )
| ( c_0 = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
thf(604,plain,
! [B: $i,A: $i] :
( ( c_uminus @ ( c_uminus @ A @ ( tc_set @ B ) ) @ ( tc_set @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( c_lessequals @ c_0 @ ( c_uminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
thf(900,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ c_0 @ A )
| ( c_lessequals @ c_0 @ ( c_uminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_uminus @ B @ A ) @ c_0 @ A )
| ( c_less @ c_0 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
thf(406,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ ( c_uminus @ B @ A ) @ c_0 @ A )
| ( c_less @ c_0 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= ( c_times @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_1) ).
thf(631,plain,
! [B: $i,A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= ( c_times @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(230,axiom,
c_lessequals @ c_0 @ c_0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_1) ).
thf(758,plain,
c_lessequals @ c_0 @ c_0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(154,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
thf(609,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_less @ ( c_plus @ B @ C @ A ) @ ( c_plus @ D @ C @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_0) ).
thf(323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_less @ ( c_plus @ B @ C @ A ) @ ( c_plus @ D @ C @ A ) @ A )
| ( c_less @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(146,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
thf(594,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(214,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
thf(726,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(199,axiom,
! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_1) ).
thf(700,plain,
! [A: $i] : ( c_lessequals @ c_emptyset @ c_emptyset @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(235,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
thf(769,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__no__zero__divisors @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).
thf(858,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ B @ A )
!= c_0 )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
thf(367,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_times @ A @ B @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(123,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Olorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
thf(552,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Olorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(162,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
thf(626,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(297,axiom,
! [B: $i,A: $i] :
( ( c_List_Olexn @ A @ c_0 @ B )
= c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
thf(915,plain,
! [B: $i,A: $i] :
( ( c_List_Olexn @ A @ c_0 @ B )
= c_emptyset ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ tc_nat )
| ( c_less @ ( c_plus @ C @ A @ tc_nat ) @ ( c_plus @ C @ B @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
thf(394,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Nat_Opower @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Nat_Opower @ c_0 @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(129,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
thf(563,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(101,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
thf(505,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(177,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
thf(658,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__comm__semiring @ A )
| ( class_Ring__and__Field_Opordered__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(296,axiom,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
thf(912,plain,
! [B: $i,A: $i] :
( ( ( c_plus @ A @ B @ tc_nat )
!= c_0 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(192,axiom,
class_OrderedGroup_Oab__group__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
thf(685,plain,
class_OrderedGroup_Oab__group__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
thf(636,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ ( c_times @ A @ C @ tc_nat ) @ ( c_times @ B @ C @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(197,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_HOL_Oabs @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
thf(695,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_HOL_Oabs @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(187,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
thf(675,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(172,axiom,
! [A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
thf(648,plain,
! [A: $i] :
( ( c_times @ c_0 @ A @ tc_nat )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(254,axiom,
! [A: $i] :
( ( c_plus @ c_0 @ A @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
thf(812,plain,
! [A: $i] :
( ( c_plus @ c_0 @ A @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(226,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
thf(749,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
thf(617,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_lessequals @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_less @ ( c_plus @ B @ D @ A ) @ ( c_plus @ C @ D @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_1) ).
thf(342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
| ~ ( c_less @ B @ C @ A )
| ( c_less @ ( c_plus @ B @ D @ A ) @ ( c_plus @ C @ D @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(76,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
thf(458,plain,
class_OrderedGroup_Ocomm__monoid__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ B @ A )
!= ( c_IntDef_Oof__int @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
thf(836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( ( c_IntDef_Oof__int @ B @ A )
!= ( c_IntDef_Oof__int @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(246,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( c_0
= ( c_uminus @ c_0 @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).
thf(795,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( c_0
= ( c_uminus @ c_0 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(189,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
thf(680,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_OrderedGroup_Onprt @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
thf(776,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_OrderedGroup_Onprt @ B @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(111,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
thf(525,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(279,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( c_lessequals @ c_0 @ ( c_plus @ B @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
thf(872,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( c_lessequals @ c_0 @ ( c_plus @ B @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
thf(707,plain,
! [C: $i,B: $i,A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( c_lessequals @ ( c_times @ B @ A @ tc_nat ) @ ( c_times @ C @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(55,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).
thf(414,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_less @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(244,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
thf(791,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(141,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
thf(585,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(79,axiom,
class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
thf(463,plain,
class_OrderedGroup_Olordered__ab__group__meet @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(120,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_times @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
thf(544,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_times @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(84,axiom,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
thf(470,plain,
! [A: $i] :
( ~ ( class_LOrder_Olorder @ A )
| ( class_LOrder_Omeet__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
!= ( c_HOL_Oabs @ B @ A ) )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
thf(576,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_0
!= ( c_HOL_Oabs @ B @ A ) )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_times @ A @ C @ tc_nat ) )
| ( B = C )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
thf(703,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= ( c_times @ A @ C @ tc_nat ) )
| ( B = C )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(150,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
thf(600,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
thf(314,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ A @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat ) @ tc_nat )
| ( c_less @ c_0 @ A @ tc_nat )
| ( ( c_Numeral_Onumber__of @ B @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
thf(497,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ~ ( c_lessequals @ ( c_times @ A @ B @ tc_nat ) @ ( c_times @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(70,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
thf(446,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ ( c_OrderedGroup_Onprt @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
thf(571,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_OrderedGroup_Onprt @ B @ A ) @ ( c_OrderedGroup_Onprt @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(81,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
thf(465,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= ( c_times @ B @ c_0 @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_1) ).
thf(450,plain,
! [B: $i,A: $i] :
( ( c_times @ A @ c_0 @ tc_nat )
= ( c_times @ B @ c_0 @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(185,axiom,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_0
= ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
thf(671,plain,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( c_0
= ( c_Numeral_Onumber__of @ A @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(194,axiom,
class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
thf(688,plain,
class_LOrder_Ojoin__semilorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(96,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
thf(495,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(231,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_OrderedGroup_Opprt @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
thf(759,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ c_0 @ B @ A )
| ( ( c_OrderedGroup_Opprt @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(287,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
thf(891,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(267,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( c_0
!= ( c_uminus @ B @ A ) )
| ( c_0 = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_0) ).
thf(844,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( c_0
!= ( c_uminus @ B @ A ) )
| ( c_0 = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_plus @ ( c_uminus @ B @ A ) @ B @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
thf(771,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_plus @ ( c_uminus @ B @ A ) @ B @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(31,axiom,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(363,plain,
! [B: $i,A: $i] :
~ ( c_less @ ( c_plus @ A @ B @ tc_nat ) @ B @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_OrderedGroup_Opprt @ B @ A ) @ ( c_OrderedGroup_Opprt @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
thf(556,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_OrderedGroup_Opprt @ B @ A ) @ ( c_OrderedGroup_Opprt @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(110,axiom,
class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
thf(524,plain,
class_Ring__and__Field_Oaxclass__no__zero__divisors @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(138,axiom,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).
thf(581,plain,
! [A: $i] : ( class_HOL_Ominus @ ( tc_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(143,axiom,
! [A: $i] :
( ( class_OrderedGroup_Omonoid__mult @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_14) ).
thf(588,plain,
! [A: $i] :
( ( class_OrderedGroup_Omonoid__mult @ ( tc_set @ A ) )
| ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(107,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_HOL_Ominus @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
thf(517,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_HOL_Ominus @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
thf(319,plain,
! [B: $i,A: $i] :
( ~ ( c_less @ c_0 @ A @ tc_nat )
| ( c_less @ c_0 @ ( c_plus @ B @ A @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Ochar_OChar @ A @ B ) @ tc_List_Ochar )
= c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
thf(896,plain,
! [B: $i,A: $i] :
( ( c_Nat_Osize @ ( c_List_Ochar_OChar @ A @ B ) @ tc_List_Ochar )
= c_0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
thf(652,plain,
! [B: $i,A: $i] :
( ( ( c_times @ A @ B @ tc_nat )
!= c_0 )
| ( B = c_0 )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
thf(390,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ~ ( c_less @ ( c_HOL_Oabs @ B @ A ) @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
thf(401,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ( c_lessequals @ A @ B @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(217,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
thf(731,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(132,axiom,
class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
thf(568,plain,
class_OrderedGroup_Opordered__ab__group__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(104,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Onprt @ c_0 @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
thf(510,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_OrderedGroup_Onprt @ c_0 @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ B @ A )
!= ( c_uminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
thf(667,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ B @ A )
!= ( c_uminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(88,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
thf(478,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ c_0 @ ( c_uminus @ B @ A ) @ A )
| ( c_less @ B @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
thf(383,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_less @ c_0 @ ( c_uminus @ B @ A ) @ A )
| ( c_less @ B @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(191,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
thf(684,plain,
class_Ring__and__Field_Oaxclass__0__neq__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
| ( c_less @ B @ C @ tc_IntDef_Oint ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
thf(346,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A )
| ( c_less @ B @ C @ tc_IntDef_Oint ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(122,axiom,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Numeral_Onumber__of @ A @ tc_nat )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_1) ).
thf(549,plain,
! [A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_Numeral_Onumber__of @ A @ tc_nat )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ochar_OChar @ A @ B )
!= ( c_List_Ochar_OChar @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
thf(536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ochar_OChar @ A @ B )
!= ( c_List_Ochar_OChar @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(208,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
thf(716,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(1,negated_conjecture,
! [A: $i] : ( c_lessequals @ ( v_lb @ A ) @ ( v_f @ A ) @ t_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(300,plain,
! [A: $i] : ( c_lessequals @ ( v_lb @ A ) @ ( v_f @ A ) @ t_b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ ( c_uminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
thf(432,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_uminus @ ( c_uminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(263,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Ojoin @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
= c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
thf(833,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( ( c_LOrder_Ojoin @ c_0 @ ( c_uminus @ c_0 @ A ) @ A )
= c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(50,axiom,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ A @ c_0 @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_2) ).
thf(405,plain,
! [A: $i] : ( c_less @ c_0 @ ( c_Nat_Opower @ A @ c_0 @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(271,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
thf(854,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Ocomm__monoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(277,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ ( c_plus @ B @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
thf(867,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ~ ( c_lessequals @ ( c_plus @ B @ B @ A ) @ c_0 @ A )
| ( c_lessequals @ B @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(276,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
thf(865,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Opordered__comm__semiring @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_less @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A )
| ( B = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
thf(373,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( c_less @ c_0 @ ( c_HOL_Oabs @ B @ A ) @ A )
| ( B = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ C @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_less @ B @ C @ tc_IntDef_Oint )
| ( c_less @ ( c_IntDef_Oof__int @ B @ A ) @ ( c_IntDef_Oof__int @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(248,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
thf(801,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__abs__if @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(66,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
thf(437,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Oupt @ B @ C ) @ tc_nat )
= ( c_List_Oupt @ ( c_plus @ B @ A @ tc_nat ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).
thf(664,plain,
! [C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Oupt @ B @ C ) @ tc_nat )
= ( c_List_Oupt @ ( c_plus @ B @ A @ tc_nat ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
thf(828,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ ( c_plus @ A @ B @ tc_nat ) @ ( c_plus @ A @ C @ tc_nat ) @ tc_nat )
| ( c_lessequals @ B @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(115,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
thf(532,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Opordered__ab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(210,axiom,
class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
thf(720,plain,
class_OrderedGroup_Olordered__ab__group @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(29,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
thf(358,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ ( c_HOL_Oabs @ c_0 @ tc_IntDef_Oint ) @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_uminus @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
thf(807,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ ( c_uminus @ C @ A ) @ ( c_uminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(86,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
thf(474,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(234,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
thf(767,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ~ ( c_IntDef_Oneg @ c_0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(285,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
thf(886,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Omonoid__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
thf(415,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
| ( class_OrderedGroup_Oab__semigroup__mult @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(80,axiom,
class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
thf(464,plain,
class_Ring__and__Field_Oaxclass__abs__if @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ A @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
thf(332,plain,
! [A: $i] :
( ~ ( c_less @ c_0 @ ( c_Nat_Opower @ c_0 @ A @ tc_nat ) @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(62,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
thf(427,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__meet @ A )
| ( class_OrderedGroup_Oab__group__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(147,axiom,
class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
thf(596,plain,
class_LOrder_Omeet__semilorder @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(170,axiom,
class_LOrder_Olorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
thf(644,plain,
class_LOrder_Olorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
= ( c_List_Odrop @ ( c_plus @ A @ B @ tc_nat ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Odrop @ A @ ( c_List_Odrop @ B @ C @ D ) @ D )
= ( c_List_Odrop @ ( c_plus @ A @ B @ tc_nat ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(294,axiom,
! [A: $i] :
( ( c_plus @ A @ c_0 @ tc_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(908,plain,
! [A: $i] :
( ( c_plus @ A @ c_0 @ tc_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(212,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
thf(723,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ A )
| ( class_LOrder_Ojoin__semilorder @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(269,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
thf(850,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_Ring__and__Field_Oaxclass__0__neq__1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(68,axiom,
class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
thf(442,plain,
class_Ring__and__Field_Opordered__comm__semiring @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(99,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
thf(501,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(34,axiom,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
thf(369,plain,
! [A: $i] :
~ ( c_less @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(161,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
thf(624,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oordered__cancel__ab__semigroup__add @ A )
| ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_plus @ c_0 @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
thf(839,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
| ( ( c_plus @ c_0 @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(215,axiom,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
thf(728,plain,
! [B: $i,A: $i] : ( c_lessequals @ c_emptyset @ A @ ( tc_set @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(221,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
thf(740,plain,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_IntDef_Oint,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_plus @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
thf(486,plain,
! [B: $i,A: $i] :
( ~ ( c_IntDef_Oneg @ ( c_Numeral_Onumber__of @ A @ tc_IntDef_Oint ) @ tc_IntDef_Oint )
| ( ( c_plus @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ ( c_Numeral_Onumber__of @ B @ tc_nat ) @ tc_nat )
= ( c_Numeral_Onumber__of @ B @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ c_0 @ ( c_OrderedGroup_Opprt @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
thf(803,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group @ A )
| ( c_lessequals @ c_0 @ ( c_OrderedGroup_Opprt @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(19,axiom,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
thf(337,plain,
! [A: $i] :
( ( c_less @ c_0 @ A @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
thf(354,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_less @ A @ B @ ( tc_set @ C ) )
| ~ ( c_lessequals @ B @ A @ ( tc_set @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
!= c_0 )
| ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_1) ).
thf(309,plain,
! [B: $i,A: $i] :
( ( ( c_Numeral_Onumber__of @ A @ tc_nat )
!= c_0 )
| ( c_less @ c_0 @ ( c_Nat_Opower @ B @ ( c_Numeral_Onumber__of @ A @ tc_nat ) @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(229,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
thf(755,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ c_0 @ tc_nat )
| ( A = c_0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(145,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
thf(592,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__join @ A )
| ( class_OrderedGroup_Olordered__ab__group @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(74,axiom,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
thf(454,plain,
! [A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( class_OrderedGroup_Ocomm__monoid__add @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(283,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
thf(882,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( class_OrderedGroup_Olordered__ab__group__meet @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(929,plain,
$false,
inference(cvc4,[status(thm)],[645,809,365,628,893,468,666,481,352,408,741,379,655,597,861,582,762,614,677,385,472,814,698,747,340,670,898,782,709,417,301,565,785,344,542,587,619,917,751,559,638,421,606,325,448,817,902,492,789,443,321,376,485,348,821,905,480,602,397,774,660,411,507,877,692,527,312,307,452,920,439,529,661,793,810,381,534,798,910,302,561,392,424,429,729,467,361,879,329,461,493,682,710,847,566,852,435,522,830,456,842,874,317,650,615,725,403,388,356,869,499,519,742,884,642,489,590,547,706,554,753,686,476,622,701,515,738,721,569,779,371,503,633,805,508,657,558,674,530,662,718,888,425,513,824,856,745,573,689,733,584,819,579,413,826,711,641,713,335,350,540,611,787,419,736,303,599,863,764,604,900,406,631,758,609,323,594,726,700,769,858,367,552,626,915,399,394,563,505,658,912,685,636,695,675,648,812,749,617,342,458,836,795,680,776,525,872,707,414,327,791,585,463,544,470,576,703,600,314,497,446,571,465,450,671,688,495,759,891,844,771,363,556,524,581,588,517,319,896,652,390,401,731,568,510,667,478,383,684,346,549,536,716,300,432,833,405,854,867,865,373,305,801,437,664,828,532,720,358,807,474,767,886,415,464,332,427,596,644,459,908,723,850,442,501,369,624,839,728,740,486,803,337,354,309,755,592,454,882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : ANA009-1 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.10 % Command : run_Leo-III %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Thu May 18 17:56:50 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.74/0.73 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.75/1.04 % [INFO] Parsing done (306ms).
% 1.75/1.05 % [INFO] Running in sequential loop mode.
% 2.25/1.28 % [INFO] eprover registered as external prover.
% 2.25/1.28 % [INFO] cvc4 registered as external prover.
% 2.25/1.29 % [INFO] Scanning for conjecture ...
% 3.01/1.47 % [INFO] Found a conjecture and 2782 axioms. Running axiom selection ...
% 3.75/1.68 % [INFO] Axiom selection finished. Selected 295 axioms (removed 2487 axioms).
% 4.29/1.78 % [INFO] Problem is propositional (TPTP CNF).
% 4.32/1.79 % [INFO] Type checking passed.
% 4.32/1.79 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 8.63/2.90 % External prover 'cvc4' found a proof!
% 8.63/2.90 % [INFO] Killing All external provers ...
% 8.63/2.90 % Time passed: 2502ms (effective reasoning time: 1854ms)
% 8.63/2.90 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.63/2.91 % Axioms used in derivation (295): clsarity_IntDef__Oint_34, cls_Nat_Onot__gr0_0, cls_OrderedGroup_Ojoin__0__eq__0_1, cls_Set_OCompl__subset__Compl__iff_1, cls_OrderedGroup_Oneg__less__iff__less_1, cls_OrderedGroup_Oneg__0__equal__iff__equal_0, cls_Power_Onat__zero__less__power__iff_2, cls_Nat_Onot__less0_0, clsrel_Ring__and__Field_Oordered__idom_32, cls_IntDef_Oof__int__le__iff_0, clsrel_OrderedGroup_Olordered__ab__group__abs_3, cls_Nat_Onat__add__left__cancel__less_1, clsrel_OrderedGroup_Olordered__ab__group__meet_1, cls_OrderedGroup_Oneg__le__iff__le_0, clsrel_OrderedGroup_Olordered__ab__group_3, cls_Nat_Onat__add__right__cancel_0, cls_IntDef_Oof__int__0__le__iff_0, clsarity_IntDef__Oint_46, clsrel_Ring__and__Field_Oordered__idom_12, cls_IntDef_Oof__int__0__less__iff_0, clsarity_IntDef__Oint_24, clsrel_OrderedGroup_Olordered__ab__group__join_3, cls_OrderedGroup_Oneg__0__le__iff__le_1, cls_OrderedGroup_Oneg__0__less__iff__less_0, cls_Nat_Omult__le__cancel1_1, clsrel_OrderedGroup_Opordered__ab__group__add_1, clsrel_Ring__and__Field_Oordered__idom_23, clsarity_IntDef__Oint_52, clsrel_OrderedGroup_Olordered__ab__group__join_6, cls_OrderedGroup_Opprt__eq__id_0, cls_OrderedGroup_Oadd__le__cancel__right_0, cls_OrderedGroup_Oneg__le__0__iff__le_1, cls_Nat_Oop_A_K_Omult__0_0, cls_OrderedGroup_Oadd__less__cancel__right_0, cls_IntDiv_Ozero__less__zpower__abs__iff_2, cls_OrderedGroup_Oabs__ge__zero_0, clsrel_Ring__and__Field_Oordered__idom_37, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13, clsarity_nat_40, clsrel_Ring__and__Field_Oordered__idom_17, cls_OrderedGroup_Oabs__not__less__zero_0, clsrel_OrderedGroup_Olordered__ab__group__join_0, cls_OrderedGroup_Ozero__less__abs__iff_0, cls_OrderedGroup_Oabs__0__eq_0, cls_NatBin_Opower__nat__number__of__number__of_0, cls_OrderedGroup_Onprt__mono_0, cls_Nat_Oadd__is__0_0, cls_LOrder_Omeet__idempotent_0, clsrel_Ring__and__Field_Oordered__idom_56, cls_OrderedGroup_Oabs__add__abs_0, cls_Nat_Oless__irrefl_0, cls_NatBin_Oeq__0__number__of_1, cls_OrderedGroup_Oneg__meet__eq__join_0, cls_Numeral_Obin__rel__simps__8_0, cls_IntDef_Oof__int__less__iff_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0, clsrel_Ring__and__Field_Oaxclass__abs__if_0, clsrel_OrderedGroup_Oab__group__add_0, cls_Nat_Omult__less__cancel2_1, cls_Nat_Omult__0__right_0, cls_Set_OCompl__eq__Compl__iff_0, clsarity_IntDef__Oint_0, clsarity_IntDef__Oint_38, cls_Set_OpsubsetI_0, cls_Set_Osubset__refl_0, cls_LOrder_Ojoin__idempotent_0, cls_Nat_Onat__add__left__cancel__le_0, cls_List_Ochar_Oinject_0, cls_OrderedGroup_Omeet__0__eq__0_0, cls_Nat_Omult__less__cancel1_1, cls_Nat_Oadd__gr__0_2, clsrel_OrderedGroup_Olordered__ab__group__abs_0, cls_Nat_Onat__add__left__cancel__less_0, cls_OrderedGroup_Oabs__eq__0_0, clsarity_nat_36, clsarity_IntDef__Oint_47, clsarity_IntDef__Oint_48, cls_Nat_Omult__le__cancel1_0, cls_IntDef_Oof__int__le__0__iff_1, cls_Set_Osubset__empty_0, clsrel_OrderedGroup_Olordered__ab__group__abs_14, clsrel_OrderedGroup_Olordered__ab__group_6, cls_Parity_Ozero__less__power__nat__eq__number__of_1, clsarity_IntDef__Oint_58, clsrel_OrderedGroup_Olordered__ab__group__abs_4, clsrel_Ring__and__Field_Oordered__idom_38, cls_Nat_Omult__less__cancel2_0, cls_Parity_Ozero__less__power__nat__eq__number__of_0, clsrel_Ring__and__Field_Oordered__idom_51, clsrel_Ring__and__Field_Oordered__idom_36, cls_OrderedGroup_Oadd__less__cancel__left_1, clsrel_Ring__and__Field_Oordered__idom_42, clsrel_Ring__and__Field_Oordered__idom_52, cls_OrderedGroup_Ozero__le__pprt_0, clsrel_OrderedGroup_Olordered__ab__group_0, cls_IntDef_Oof__int__less__iff_1, clsrel_OrderedGroup_Olordered__ab__group__join_17, cls_Nat_Oadd__is__0_1, cls_OrderedGroup_Oneg__0__less__iff__less_1, cls_OrderedGroup_Ojoin__0__eq__0_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12, cls_Nat_Omult__le__cancel2_2, clsrel_OrderedGroup_Olordered__ab__group__meet_5, clsrel_OrderedGroup_Olordered__ab__group_17, cls_Set_OCompl__subset__Compl__iff_0, clsarity_set_12, cls_IntDef_Oof__int__0__le__iff_1, cls_Nat_Omult__cancel1_1, cls_OrderedGroup_Onprt__le__zero_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10, cls_Nat_Onat__0__less__mult__iff_0, cls_IntDiv_Ozero__less__zpower__abs__iff_1, cls_IntDef_Oof__int__eq__iff_0, cls_IntDef_Oof__int__0__eq__iff_0, cls_Nat_Ole__0__eq_0, cls_Ring__and__Field_Omult__cancel__right1_1, clsrel_Ring__and__Field_Opordered__comm__semiring_2, cls_OrderedGroup_Oneg__le__iff__le_1, cls_Set_Oempty__subsetI_0, cls_List_Odrop__0_0, clsrel_OrderedGroup_Oab__group__add_1, clsrel_Ring__and__Field_Oordered__idom_11, cls_Ring__and__Field_Omult__cancel__left1_1, clsrel_OrderedGroup_Olordered__ab__group__meet_6, clsrel_OrderedGroup_Olordered__ab__group__meet_17, clsarity_nat_37, cls_Nat_Omult__cancel2_0, clsrel_LOrder_Olorder_0, cls_Set_Osubset__antisym_0, cls_Nat_Onat__add__left__cancel__le_1, clsarity_set_14, cls_Nat_Omult__less__cancel1_0, clsarity_IntDef__Oint_37, clsrel_OrderedGroup_Opordered__ab__group__add_2, clsarity_nat_6, cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0, cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0, cls_NatBin_Oeq__nat__number__of_10, cls_OrderedGroup_Opprt__0_0, clsrel_OrderedGroup_Olordered__ab__group__abs_16, cls_Nat_Onat__0__less__mult__iff_1, cls_Set_Osubset__empty_1, clsrel_OrderedGroup_Olordered__ab__group__abs_15, clsrel_OrderedGroup_Olordered__ab__group_1, clsrel_OrderedGroup_Olordered__ab__group__meet_15, clsrel_OrderedGroup_Olordered__ab__group_5, cls_Nat_Omult__cancel2_1, clsrel_OrderedGroup_Olordered__ab__group__abs_6, clsarity_nat_34, cls_Parity_Ozero__less__power__nat__eq__number__of_2, cls_OrderedGroup_Ominus__minus_0, clsrel_Ring__and__Field_Oordered__idom_46, cls_OrderedGroup_Oabs__of__nonpos_0, cls_OrderedGroup_Oneg__equal__0__iff__equal_0, clsarity_nat_17, cls_NatBin_Omult__nat__number__of_0, cls_IntDef_Oof__int__less__0__iff_0, cls_OrderedGroup_Opprt__eq__0_0, cls_NatBin_Oadd__nat__number__of_1, clsarity_IntDef__Oint_54, clsrel_Ring__and__Field_Oordered__idom_53, clsarity_IntDef__Oint_40, clsrel_OrderedGroup_Olordered__ab__group__join_16, clsrel_Ring__and__Field_Oordered__idom_35, cls_OrderedGroup_Oadd__le__cancel__left_0, cls_OrderedGroup_Opprt__mono_0, clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11, cls_Nat_Oadd__gr__0_0, cls_OrderedGroup_Oabs__minus__cancel_0, clsarity_nat_23, cls_OrderedGroup_Onprt__eq__id_0, cls_OrderedGroup_Onprt__eq__0_0, clsrel_Ring__and__Field_Oordered__idom_50, cls_Nat_Onot__add__less1_0, cls_OrderedGroup_Ozero__less__abs__iff_1, clsrel_OrderedGroup_Olordered__ab__group__abs_1, cls_Nat_Oadd__is__0_2, cls_OrderedGroup_Oadd__le__cancel__right_1, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0, clsrel_OrderedGroup_Olordered__ab__group_15, clsrel_Ring__and__Field_Oordered__idom_41, cls_Nat_Omult__cancel1_0, clsarity_IntDef__Oint_32, cls_OrderedGroup_Oabs__eq__0_1, cls_OrderedGroup_Oadd__less__cancel__right_1, clsrel_OrderedGroup_Olordered__ab__group__meet_18, clsrel_OrderedGroup_Olordered__ab__group_16, cls_OrderedGroup_Oabs__le__zero__iff_0, clsrel_OrderedGroup_Olordered__ab__group__join_2, clsarity_IntDef__Oint_22, cls_Nat_Omult__le__cancel2_1, clsarity_nat_20, cls_OrderedGroup_Oneg__less__0__iff__less_1, cls_Nat_Oadd__0__right_0, clsrel_Ring__and__Field_Opordered__semiring_4, clsarity_nat_5, cls_OrderedGroup_Oadd__less__cancel__left_0, cls_Power_Onat__zero__less__power__iff_1, cls_Set_OpsubsetE_0, clsrel_Ring__and__Field_Oordered__idom_8, clsrel_OrderedGroup_Olordered__ab__group__meet_3, cls_IntDiv_Ozero__less__zpower__abs__iff_0, cls_Nat_Onot__gr0_1, clsarity_IntDef__Oint_43, cls_OrderedGroup_Ominus__add__distrib_0, cls_Nat_Onot__add__less2_0, clsarity_set_13, clsrel_Ring__and__Field_Opordered__comm__semiring_15, clsarity_nat_9, cls_OrderedGroup_Oadd__0__right_0, cls_IntDef_Oof__int__eq__0__iff_0, cls_OrderedGroup_Oneg__less__iff__less_0, clsarity_IntDef__Oint_33, clsrel_Ring__and__Field_Oordered__idom_4, clsrel_OrderedGroup_Olordered__ab__group__meet_16, clsarity_nat_35, cls_OrderedGroup_Oneg__0__equal__iff__equal_1, cls_IntDef_Oof__int__le__iff_1, cls_IntDef_Oof__int__le__0__iff_0, clsrel_OrderedGroup_Opordered__ab__group__add_13, cls_OrderedGroup_Oabs__0__eq_1, clsarity_IntDef__Oint_17, cls_OrderedGroup_Onprt__0_0, clsrel_Ring__and__Field_Oordered__idom_54, clsrel_OrderedGroup_Olordered__ab__group_2, cls_IntDef_Oof__int__less__0__iff_1, cls_Nat_Omult__less__cancel1_2, cls_OrderedGroup_Oneg__equal__0__iff__equal_1, cls_IntDef_Oof__int__0__less__iff_1, cls_OrderedGroup_Oright__minus_0, cls_IntDiv_Ozero__le__zpower__abs_0, clsrel_OrderedGroup_Olordered__ab__group__abs_7, clsrel_OrderedGroup_Opordered__ab__group__add_0, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1, cls_Nat_Onat__add__left__cancel_0, cls_IntDef_Oof__int__0__eq__iff_1, cls_Nat_Onat__0__less__mult__iff_2, clsarity_IntDef__Oint_39, clsrel_OrderedGroup_Olordered__ab__group__abs_2, clsarity_nat_13, clsrel_Ring__and__Field_Oordered__idom_34, cls_OrderedGroup_Oneg__equal__iff__equal_0, clsrel_OrderedGroup_Olordered__ab__group__join_15, clsarity_nat_24, cls_List_Olexn_Osimps__1_0, cls_OrderedGroup_Oneg__le__0__iff__le_0, clsarity_IntDef__Oint_51, cls_OrderedGroup_Oadd__le__cancel__left_1, clsarity_set_0, clsrel_OrderedGroup_Ocomm__monoid__mult_1, clsrel_OrderedGroup_Olordered__ab__group__meet_0, cls_Nat_Ole0_0, clsarity_nat_4, cls_OrderedGroup_Oneg__0__le__iff__le_0, cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0, cls_NatBin_Oadd__nat__number__of_0, cls_Nat_Oop_A_L_Oadd__0_0, clsarity_IntDef__Oint_23, clsrel_OrderedGroup_Ocomm__monoid__mult_4, cls_Nat_Oadd__gr__0_1, cls_Set_Onot__psubset__empty_0, cls_Nat_Ole__0__eq_1, clsarity_IntDef__Oint_50, cls_List_Ochar_Oinject_1, cls_OrderedGroup_Oabs__of__nonneg_0, clsarity_IntDef__Oint_12, clsrel_OrderedGroup_Opordered__ab__group__add_12, cls_OrderedGroup_Oneg__less__0__iff__less_0, clsrel_LOrder_Olorder_3, clsrel_Ring__and__Field_Oordered__idom_5, clsrel_OrderedGroup_Olordered__ab__group__join_5, cls_Nat_Omult__le__cancel1_2, cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1, cls_Set_OpsubsetE_1, cls_Nat_Omult__le__cancel2_0, clsrel_OrderedGroup_Olordered__ab__group__meet_2, clsrel_Ring__and__Field_Opordered__comm__semiring_7, cls_IntDef_Oof__int__eq__0__iff_1, cls_OrderedGroup_Oabs__idempotent_0, cls_Set_Odouble__complement_0, cls_Nat_Omult__less__cancel2_2, cls_List_Odrop__upt_0, cls_NatBin_Oeq__number__of__0_1, cls_OrderedGroup_Oabs__le__zero__iff_1, cls_Nat_Omult__is__0_0, cls_List_Ochar_Osize_0, clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0, cls_OrderedGroup_Omeet__0__eq__0_1, cls_OrderedGroup_Oneg__join__eq__meet_0, clsrel_OrderedGroup_Olordered__ab__group__join_1, clsarity_IntDef__Oint_9, cls_Power_Onat__zero__less__power__iff_0, clsrel_OrderedGroup_Olordered__ab__group__join_18, clsarity_set_15, cls_List_Odrop__drop_0
% 8.63/2.91 % No. of inferences in proof: 599
% 8.63/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2502 ms resp. 1854 ms w/o parsing
% 8.91/3.02 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.91/3.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------